Tangent Line to an Integral Function

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The function $F$ is defined by $F(x)=\int_{1}^{x}\frac{1}{t}\, dt$ . What is an equation of the line tangent to the graph of $F$ at $x=e$ ?

$y=\frac{1}{e}x$

$y=x-e+1$

$y=\frac{1}{e}x-\frac{1}{e}+1$

$y=\frac{1}{e}$

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